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Show 83 ... • vuamque i*ter:, cipercntur , feu quints die~ ar· cus meridiani i oter vertices af fumptorum lo· corum. & quitlis h~c obferua· tio fie ret in fu· ' perficie tcru:, ob cxiguam ta: men etus parut· tatem refpeau firmamEci, perinde eft, ac 11 in ' centro hcrhur. lttdC'm prort ~ r· ea arcum,C S,in cxlo duo radij op f1 ci J eu vifiui, ad fcnfum com· p;·c h:!ndunr , li· ue ex G , in fupefficie, fiue ex cen tr? X, c gredian~ur. q·1or j~~tur .gradu: ·nat cu c s inuenieb:mt, tot etiam JO arcu rerreHn G H, cctht r:e~l necef. ,b rio con' cl'u debant; ponamus, v.g. fu1· rr·e gra.J. t·.n arcu c ·s ' tgl tur rre.s C\uoquc in arcu G H, tc·rrefhi continebantur: quo m crcs ,requas P.ar_ces dt ui f9, wadurn etiam vnum in ter:a explorat~lm hab~erunr. hunc t~Jt~r ~. .~ (og·11tum po-:lea per fradia mettcbantur: et qua: vm con.ucne:e fiadl~ ~;; re, 1 t r t ; mil\iaria vero I 3 8. quia vcro maxt m~s terrx.am~It~ S con . ar, .. 6o, partibus , ideo pra:diaum numerum fbd10rum multtpllcantes per ~ lio,totius tcrrcni circuli ambitum c6rincre repererunt !l:ad1~ 400 s00 ~,' ideR, qu:tdringenta millia, qucr effi(iunc milli aria , 5o, oco ; 1deH 'q.utn· qu Jgintl mi~lia; ~c Ar}ft: ad finem . ~-de ca:lo_fic ~t fen; ~at.h c ~att~C~· 1 um eriam, Jnqutr, qut ctrcumfaentta: magmrudmem rattocwan tcr,tat ~cl t; oo, dicunt efl·! ftadiorum mil ia. . .. E:.mdem quantitatem vetercs ali j fyderum obrerua :orcs a~ i.1> 0mth ta· m~n via compcrerur.t ;nam ex duobus djuerGs locis Poli altJrudmes ?b·, feru aret1t:, co rnodo quem in meridiano circulo expofuimus ; qua: biOct tt 1ticudines nc ct fhrio tanto meridiani arcu difcrepa bat, quanrus quoqu.F erar :ncrs errdb is mcridiani inter eadem duo loca interiedus; quahs. t\ cJd [111 fig ura dfet :>.rcns S D,diffcrentia altitudinem poli locorum H,I, ;l1ui t:1ows dt . l1U:tn .. us eft arcus HI, inter eadem toea contentus; qu?c e·Aim gradi.tS quifpi<Lm Jmb_ulis ab H)itl I, in terra obiret, tor idem gradJb· ei po!us, ,. . -....., s, Np~tus, D, fupra ~Hum horizontem C F, elcu~retttr .; quin etiam eidcn'i honzon fuccefliue permucatur, ·quou!que li.; m.hon~onte C f. cognito igitur p~r quad~ A~tem arcu S D, cogOJt~s quoque e:t~ ar~us, H I, ia gra .. dibus. d1menf~ JESlt~r arcu~H I, per ltadta,_vel per m~ll!a_rta, pate hat quoc vnus gradUi mdbana contmerct. acquc ht duo modt Ytt faciliores , ita.... prifcis illis, ac minus cxercitatis prius occurrerunt. Vcrum poft: prifcos hofcc indagatores fubtiliori admodum via terre~ ftrcm ambitum Eratofthcncs indagauit: is auteRl Alexandria: in £gypto ancc Chrifti natalcm annis circitcr, 1jo, Syderali fcienciz nauabat ope• ram. huius i&itur rei caufa, dua~ elegit vrbes, quz fub eodcm etftnt meJ ridiano, Alcxandriam , &. Syenem; quarum Syene quz auftralior ~~, fi..:. ta~ftpracisi (ub Cancri ~ropi~o: Alexa?dria: lileinde _in platca quapiam fa tiS magna, haft am honzontl perpendicularem crextt; poftea zttiui fol~ fticij tempore, qao fcilic ec fol Cancri tropicum per currie, ac proinde in.... meridic dirc~c fupra Syenem imminet, fiue ei fit verticali', vnde & ra .. dios ci pcrpcndicul~ritcr demittit, codem inquam tempore, &·qutdeill....l .~aA~ mcridiaco, meridianam haR:a: illius Aiexandriz credz vmbrarn.... o cruauit, &. diligcntcr angulum notauit , quem foJis radiu5 per h1lh: vcr iccm tranficns , cum ipfa hafta confticuebat; cumq; quoc gr~dib.conftar- ct accurat~ txpedit.quz vt probe pr~cipiantur fit figura feques in qua (C)}, E F, terra G A 8, fitquc arcus G A B , fub meridiano Alexandriz, ~ Sycncs communi.Alcxandria Cit vbi A, Sycnc vbi B,.fub Cancro. Sol~ i&icur Cancri tropicum obeuntc, eric [otis radius in meridic ipli Syen~ ad pcrpcndict~lum, qui fit in 6gura F B , defccndatque vfque ad centrum terra C. Hafta Alcxandriz ereB:a fit AD, qu2 fimili.ccr ad centrum, C, cum radio F B C, concurrat: cod em tempore fobs alter radius per haftz apiccm, D,. tranfiens fit ED G. duos hofce radios abfque fcnfibiJi e~rore, ob nimiam folis a ttrra diftantii fupponebat cffe parallelos. quJbus prz .. notatis fie ratiocinabatur; cum linea, D A C, incidat in duas paralldas ED G, F B C, crunt per 19. primi EJe. duo anguli aJterni G D A, A C B, ~qualcs. quod ctiam patebit fi vtcrque expcndatur per propof. 1. • .A.ppar. cle~cripto videlicet arcu, A I, ex centro D~ coque in grad us diuifo; quot enun gradus in co erunt, tot neceffari& 10 arcu ttrrz A B, die neceffe eft, cum angulo, C, fubt~ndarur, qui angulo, D, zqualis efi;& proinde erunt ar~~ limiters, vt in prima propo6tionc Apparatus exp! ica rum ell:. c0gni· co Jgttur angulo D, a~ baftz veniccm, cogoofcitnr eti:im,quod lane mirum eft, angulus, C, quamuis fit in terrz centro, arque abyllo decrufus; quarcctiam innotefcit quantitas arcus, A B, meridiaRi inter Alexandria &Sycncm, quot fc:ilicet gradus contineat. tradit au tern CJeomedes in... futs Mct~oris, Eratofthencm reperifie hunc arc urn graduum 8 f . idem ~reus~ 8, quz eft diftantia przdictarum v~bium, cognicus erat etiam.... an~adtJS '. coatincbat cnim ftadia 618 J +. vnde· arichmeticis rationibus ~IgraduJ, 7oo, fta&lia, ac proindc toti tc:rri: perimetro, :J z. looo , fladia M attribuit • |
